A pressure vessel surveillance program requires a methodology for relating radiation-induced changes in materials exposed in accelerated surveillance locations to the condition of the pressure vessel (see Practice E853). An important consideration is that the irradiation exposures be expressed in a unit that is physically related to the damage mechanisms.

A major source of neutron radiation damage in metals is the displacement of atoms from their normal lattice sites. Hence, an appropriate damage exposure index is the number of times, on the average, that an atom has been displaced during an irradiation. This can be expressed as the total number of displaced atoms per unit volume, per unit mass, or per atom of the material. Displacements per atom is the most common way of expressing this quantity. The number of dpa associated with a particular irradiation depends on the amount of energy deposited in the material by the neutrons, and hence, depends on the neutron spectrum. (For a more extended discussion, see Practice E521.)

No simple correspondence exists in general between dpa and a particular change in a material property. A reasonable starting point, however, for relative correlations of property changes produced in different neutron spectra is the dpa value associated with each environment. That is, the dpa values themselves provide a spectrum-sensitive index that may be a useful correlation parameter, or some function of the dpa values may affect correlation.

TABLE 1 ENDF/B-VI-based Iron Displacement Cross Section

Bin

EngA (MeV)

σd (barns)

Bin

EngA (MeV)

σd (barns)

Bin

EngA (MeV)

σd (barns)

1

0.100E-09

158.3543

2

0.1050E-09

154.6209

3

0.110E-09

151.1395

4

0.1150E-09

147.8895

5

0.120E-09

144.1054

6

0.1275E-09

139.9202

7

0.1350E-09

136.0860

8

0.1425E-09

132.5445

9

0.150E-09

128.7502

10

0.160E-09

124.7860

11

0.170E-09

121.1728

12

0.180E-09

117.8527

13

0.190E-09

114.8137

14

0.200E-09

111.9561

15

0.210E-09

109.3199

16

0.220E-09

106.8646

17

0.230E-09

104.5694

18

0.240E-09

101.8930

19

0.2550E-09

98.93331

20

0.270E-09

96.65981

21

0.280E-09

94.12717

22

0.300E-09

91.05218

23

0.320E-09

88.24872

24

0.340E-09

85.68787

25

0.360E-09

83.33912

26

0.380E-09

81.17265

27

0.400E-09

78.92472

28

0.4250E-09

76.63646

29

0.450E-09

74.53734

30

0.4750E-09

72.59930

31

0.500E-09

70.81827

32

0.5250E-09

69.14790

33

0.550E-09

67.59222

34

0.5750E-09

66.13822

35

0.600E-09

64.64189

36

0.630E-09

63.12039

37

0.660E-09

61.70157

38

0.690E-09

60.37332

39

0.720E-09

58.92732

40

0.760E-09

57.39681

41

0.800E-09

55.97892

42

0.840E-09

54.65984

43

0.880E-09

53.43220

44

0.920E-09

52.28703

45

0.960E-09

51.21545

46

0.100E-08

50.07727

47

0.1050E-08

48.89598

48

0.110E-08

47.79609

49

0.1150E-08

46.76870

50

0.120E-08

45.57125

51

0.1275E-08

44.25006

52

0.1350E-08

43.03653

53

0.1425E-08

41.91761

54

0.150E-08

40.71708

55

0.160E-08

39.46333

56

0.170E-08

38.32018

57

0.180E-08

37.26968

58

0.190E-08

36.30967

59

0.200E-08

35.40710

60

0.210E-08

34.57391

61

0.220E-08

33.79705

62

0.230E-08

33.06956

63

0.240E-08

32.22424

64

0.2550E-08

31.28942

65

0.270E-08

30.57002

66

0.280E-08

29.76999

67

0.300E-08

28.79791

68

0.320E-08

27.91048

69

0.340E-08

27.10139

70

0.360E-08

26.35879

71

0.380E-08

25.67357

72

0.400E-08

24.96309

73

0.4250E-08

24.23960

74

0.450E-08

23.57548

75

0.4750E-08

22.96268

76

0.500E-08

22.39920

77

0.5250E-08

21.87094

78

0.550E-08

21.37982

79

0.5750E-08

20.91994

80

0.600E-08

20.44705

81

0.630E-08

19.96509

82

0.660E-08

19.51724

83

0.690E-08

19.09670

84

0.720E-08

18.63984

85

0.760E-08

18.15581

86

0.800E-08

17.70708

87

0.840E-08

17.29049

88

0.880E-08

16.90205

89

0.920E-08

16.54074

90

0.960E-08

16.20166

91

0.100E-07

15.84242

92

0.1050E-07

15.46908

93

0.110E-07

15.12094

94

0.1150E-07

14.79594

95

0.120E-07

14.41855

96

0.1275E-07

14.00095

97

0.13050E-07

13.61661

98

0.1425E-07

13.26338

99

0.150E-07

12.88403

100

0.160E-07

12.48759

101

0.170E-07

12.12633

102

0.180E-07

11.79428

103

0.190E-07

11.49039

104

0.200E-07

11.20760

105

0.210E-07

10.94298

106

0.220E-07

10.69745

107

0.230E-07

10.46804

108

0.240E-07

10.20132

109

0.2550E-07

9.906717

110

0.270E-07

9.679449

111

0.280E-07

9.427035

112

0.300E-07

9.118745

113

0.320E-07

8.838819

114

0.340E-07

8.582926

115

0.360E-07

8.347962

116

0.380E-07

8.131618

117

0.400E-07

7.907534

118

0.4250E-07

7.678809

119

0.450E-07

7.468805

120

0.4750E-07

7.276812

121

0.500E-07

7.097598

122

0.5250E-07

6.930767

123

0.550E-07

6.775607

124

0.5750E-07

6.630701

125

0.600E-07

6.482083

126

0.630E-07

6.330435

127

0.660E-07

6.188963

128

0.690E-07

6.056631

129

0.720E-07

5.913148

130

0.760E-07

5.760298

131

0.800E-07

5.618617

132

0.840E-07

5.486900

133

0.880E-07

5.364337

134

0.920E-07

5.250029

135

0.960E-07

5.143171

136

0.100E-06

5.029254

137

0.1050E-06

4.911427

138

0.110E-06

4.801945

139

0.1150E-06

4.699714

140

0.120E-06

4.581585

141

0.1275E-06

4.450361

142

0.1350E-06

4.329614

143

0.1425E-06

4.218222

144

0.150E-06

4.099185

145

0.160E-06

3.974304

146

0.170E-06

3.860402

147

0.180E-06

3.756055

148

0.190E-06

3.660761

149

0.200E-06

3.571313

150

0.210E-06

3.488699

151

0.220E-06

3.411616

152

0.230E-06

3.339466

153

0.240E-06

3.256051

154

0.2550E-06

3.163276

155

0.270E-06

3.091628

156

0.280E-06

3.013147

157

0.300E-06

2.916945

158

0.320E-06

2.829403

159

0.340E-06

2.749808

160

0.360E-06

2.676750

161

0.380E-06

2.608835

162

0.400E-06

2.527930

163

0.4250E-06

2.440897

164

0.450E-06

2.374384

165

0.4750E-06

2.313606

166

0.500E-06

2.257462

167

0.5250E-06

2.205331

168

0.550E-06

2.154114

169

0.5750E-06

2.108733

170

0.600E-06

2.060134

171

0.630E-06

2.011735

172

0.660E-06

1.966045

173

0.690E-06

1.923586

174

0.720E-06

1.877395

175

0.760E-06

1.828596

176

0.800E-06

1.783008

177

0.840E-06

1.741254

178

0.880E-06

1.703417

179

0.920E-06

1.667792

180

0.960E-06

1.632082

181

0.100E-05

1.595754

182

0.1050E-05

1.558720

183

0.110E-05

1.522295

184

0.1150E-05

1.490200

185

0.120E-05

1.451554

186

0.1275E-05

1.409592

187

0.1350E-05

1.370247

188

0.1425E-05

1.334635

189

0.150E-05

1.296298

190

0.160E-05

1.256143

191

0.170E-05

1.219824

192

0.180E-05

1.187621

193

0.190E-05

1.156028

194

0.200E-05

1.126746

195

0.210E-05

1.099981

196

0.220E-05

1.075226

197

0.230E-05

1.051885

198

0.240E-05

1.026221

199

0.2550E-05

0.9965719

200

0.270E-05

0.9722222

201

0.280E-05

0.9476671

202

0.300E-05

0.9157118

203

0.320E-05

0.8876799

204

0.340E-05

0.8611951

205

0.360E-05

0.8377314

206

0.380E-05

0.8153836

207

0.400E-05

0.7928756

208

0.4250E-05

0.7695923

209

0.450E-05

0.7481711

210

0.4750E-05

0.7286609

211

0.500E-05

0.7107515

212

0.5250E-05

0.6941600

213

0.550E-05

0.6778895

214

0.5750E-05

0.6635014

215

0.600E-05

0.6480775

216

0.630E-05

0.6327240

217

0.660E-05

0.6182052

218

0.690E-05

0.6047435

219

0.720E-05

0.5900444

220

0.760E-05

0.5745604

221

0.800E-05

0.5600318

222

0.840E-05

0.5467011

223

0.880E-05

0.5345984

224

0.920E-05

0.5232391

225

0.960E-05

0.5118709

226

0.100E-04

0.5002917

227

0.1050E-04

0.4884902

228

0.110E-04

0.4769112

229

0.1150E-04

0.4666898

230

0.120E-04

0.4543560

231

0.1275E-04

0.4409762

232

0.1350E-04

0.4284223

233

0.1425E-04

0.4170648

234

0.150E-04

0.4048129

235

0.160E-04

0.3919477

236

0.170E-04

0.3802993

237

0.180E-04

0.3699498

238

0.190E-04

0.3598211

239

0.200E-04

0.3504475

240

0.210E-04

0.3418580

241

0.220E-04

0.3339029

242

0.230E-04

0.3263810

243

0.240E-04

0.3181047

244

0.2550E-04

0.3085413

245

0.270E-04

0.3006880

246

0.280E-04

0.2927655

247

0.300E-04

0.2824593

248

0.320E-04

0.2733916

249

0.340E-04

0.2648267

250

0.360E-04

0.2572175

251

0.380E-04

0.2499703

252

0.400E-04

0.2426542

253

0.4250E-04

0.2350771

254

0.450E-04

0.2280936

255

0.4750E-04

0.2217044

256

0.500E-04

0.2158471

257

0.5250E-04

0.2104036

258

0.550E-04

0.2050605

259

0.5750E-04

0.2003403

260

0.600E-04

0.1952700

261

0.630E-04

0.1902102

262

0.660E-04

0.1854221

263

0.690E-04

0.1809756

264

0.720E-04

0.1761094

265

0.760E-04

0.1709726

266

0.800E-04

0.1661474

267

0.840E-04

0.1616956

268

0.880E-04

0.1576549

269

0.920E-04

0.1538460

270

0.960E-04

0.1500470

271

0.100E-03

0.1461601

272

0.1050E-03

0.1421933

273

0.110E-03

0.1382971

274

0.1150E-03

0.1348528

275

0.120E-03

0.1306799

276

0.1275E-03

0.1261477

277

0.1350E-03

0.1218873

278

0.1425E-03

0.1180186

279

0.150E-03

0.1138330

280

0.160E-03

0.1094287

281

0.170E-03

0.1054279

282

0.180E-03

0.1018602

283

0.190E-03

0.9837523E-01

284

0.200E-03

0.9515446E-01

285

0.210E-03

0.9224781E-01

286

0.220E-03

0.1048459

287

0.230E-03

0.1028288

288

0.240E-03

0.8397242E-01

289

0.2550E-03

0.8057346E-01

290

0.270E-03

0.7782596E-01

291

0.280E-03

0.7506079E-01

292

0.300E-03

0.7147984E-01

293

0.320E-03

0.6842791E-01

294

0.340E-03

0.1581741

295

0.360E-03

0.7452445E-01

296

0.380E-03

0.6020231E-01

297

0.400E-03

0.5752645E-01

298

0.4250E-03

0.5484677E-01

299

0.450E-03

0.5239946E-01

300

0.4750E-03

0.5017326E-01

301

0.500E-03

0.4855164E-01

302

0.5250E-03

0.4750492E-01

303

0.550E-03

0.8634498E-01

304

0.5750E-03

0.3684567

305

0.600E-03

0.7230662

306

0.630E-03

1.085166

307

0.660E-03

1.433057

308

0.690E-03

1.753764

309

0.720E-03

2.100540

310

0.760E-03

2.428895

311

0.800E-03

2.722788

312

0.840E-03

2.998771

313

0.880E-03

3.258461

314

0.920E-03

3.465372

315

0.960E-03

3.618973

316

0.100E-02

3.787081

317

0.1050E-02

3.964271

318

0.110E-02

13.13789

319

0.1150E-02

10.69382

320

0.120E-02

4.262693

321

0.1275E-02

4.338387

322

0.1350E-02

4.435367

323

0.1425E-02

4.534225

324

0.150E-02

4.592575

325

0.160E-02

4.783180

326

0.170E-02

4.701623

327

0.180E-02

4.841220

328

0.190E-02

4.999009

329

0.200E-02

5.111335

330

0.201E-02

5.183993

331

0.220E-02

5.279069

332

0.230E-02

5.408910

333

0.240E-02

5.523736

334

0.2550E-02

5.695442

335

0.270E-02

5.826853

336

0.280E-02

5.975410

337

0.300E-02

6.173523

338

0.320E-02

6.395415

339

0.340E-02

6.658582

340

0.360E-02

7.183939

341

0.380E-02

10.01168

342

0.400E-02

9.194485

343

0.4250E-02

8.178266

344

0.450E-02

8.229657

345

0.4750E-02

8.508525

346

0.500E-02

8.910876

347

0.5250E-02

9.525395

348

0.550E-02

10.59739

349

0.5750E-02

13.20411

350

0.600E-02

21.17466

351

0.630E-02

19.67340

352

0.660E-02

18.59203

353

0.690E-02

24.36627

354

0.720E-02

39.42936

355

0.760E-02

56.38621

356

0.800E-02

48.66102

357

0.840E-02

35.11790

358

0.880E-02

27.24892

359

0.920E-02

23.52159

1. Scope

1.1 This practice describes a standard procedure for characterizing neutron irradiations of iron (and low alloy steels) in terms of the exposure index displacements per atom (dpa) for iron.

1.2 Although the methods of this practice apply to any material for which a displacement cross section σd(E) is known (see Practice E521), this practice is written specifically for iron.

1.3 It is assumed that the displacement cross section for iron is an adequate approximation for calculating displacements in steels that are mostly iron (95 to 100 %) in radiation fields for which secondary damage processes are not important.

1.4 Procedures analogous to this one can be formulated for calculating dpa in charged particle irradiations. (See Practice E521.)

1.5 The application of this practice requires knowledge of the total neutron fluence and flux spectrum. Refer to Practice E521 for determining these quantities.

1.6 The correlation of radiation effects data is beyond the scope of this practice.

1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.